Split balance weights for eliminating density effect on flow

ABSTRACT

A Coriolis flow meter includes at least one flow conduit ( 103 ), including a first conduit node ( 603   a ) and a second conduit node ( 603   b ) and a bending axis W that intersects the flow conduit ( 103 ) at the first conduit node ( 603   a ) and at the second conduit node ( 603   b ). The flow conduit ( 103 ) vibrates around the bending axis W. The meter further includes a drive system ( 104 ) and a balance system ( 600 ) coupled to the flow conduit ( 103 ). The balance system ( 600 ) includes two or more Y-balance weights ( 601   a,    601   b ) and two or more attachment members ( 602   a,    602   b ) that couple the two or more Y-balance weights ( 601   a,    601   b ) to the flow conduit ( 103 ). At least a first Y-balance weight ( 601   a ) is coupled to the flow conduit ( 103 ) at a first location between the first conduit node ( 603   a ) and the drive system ( 104 ) and at least a second Y-balance weight ( 601   b ) is coupled to the flow conduit ( 103 ) at a second location between the drive system ( 104 ) and the second conduit node ( 603   b ).

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to force balancing a Coriolis flow meterusing two or more split Y-balance weights.

2. Statement of the Problem

Vibrating conduit sensors, such as Coriolis mass flow meters, typicallyoperate by detecting motion of a vibrating conduit that contains amaterial. Properties associated with the material in the conduit, suchas mass flow, density and the like, in the conduit may be determined byprocessing signals from motion transducers associated with the conduit,as the vibration modes of the vibrating material-filled system generallyare affected by the combined mass, stiffness and damping characteristicsof the containing conduit and the material contained therein.

A typical Coriolis mass flow meter includes one or more conduits thatare connected inline in a pipeline or other transport system and conveymaterial, e.g., fluids, slurries and the like, in the system. Eachconduit may be viewed as having a set of natural vibration modesincluding, for example, simple bending, torsional, radial, and coupledmodes. In a typical Coriolis mass flow measurement application, aconduit is excited in one or more vibration modes as a material flowsthrough the conduit, and motion of the conduit is measured at pointsspaced along the conduit. Excitation is typically provided by anactuator, e.g., an electromechanical device, such as a voice coil-typedriver, that perturbs the conduit in a periodic fashion. Mass flow ratemay be determined by measuring time delay or phase differences betweenmotions at the transducer locations.

The magnitude of the time delay is very small; often measured innanoseconds. Therefore, it is necessary to have the transducer output bevery accurate. Transducer accuracy may be compromised by nonlinearitiesand asymmetries in the meter structure or from motion arising fromextraneous forces. For example, a Coriolis mass flow meter havingunbalanced components can vibrate its case, flanges and the pipeline atthe drive frequency of the meter. This vibration perturbs the time delaysignal in an amount that depends on the rigidity of the mount.Additionally, a Coriolis flow meter determines the density of the flowmaterial based on the frequency of the drive mode. If the drive modeincludes motion of the case, flanges, and pipeline, the performance ofthe density measurement can be adversely affected. Since the rigidity ofthe mount is generally unknown and can change over time and temperature,the effects of the unbalanced components cannot be compensated and maysignificantly affect meter performance. The effects of these unbalancedvibrations and mounting variations are reduced by using flow meterdesigns that are balanced and by using signal processing techniques tocompensate for unwanted components of motion.

The balanced vibration discussed above involves only a single directionof vibration: the Z-direction. The Z-direction is the direction that theconduits are displaced as they vibrate. Other directions, including theX-direction along the pipeline and the Y-direction perpendicular to theZ and X-directions, are not balanced. This reference coordinate systemis important because Coriolis flow meters produce a secondary sinusoidalforce in the Y-direction. This force creates a meter vibration in theY-direction that is not balanced, resulting in meter error.

One source of this secondary force is the location of the mass of themeter driver assembly. A typical driver assembly consists of a magnetfastened to one conduit and a coil of conductive wire fastened toanother conduit. The Y-vibration is caused by the center of mass of thedriver magnet and the center of mass of the driver coil not lying on therespective X-Y planes of the centerline(s) of the flow conduit(s). TheX-Y planes are necessarily spaced apart to keep the conduits frominterfering with one another. The centers of mass of the magnet and/orcoil are offset from their planes because the coil needs to beconcentric with the end of magnet to be at the optimum position in themagnetic field.

A flow conduit, when driven to vibrate, does not truly translate butrather cyclically bends about the locations at which it is fixed. Thisbending can be approximated by rotation about the fixed point(s). Thevibration is then seen to be a cyclic rotation through a small angleabout its center of rotation, CR. The angular vibration amplitude isdetermined from the desired vibration amplitude in the Z direction andthe distance, d, from the center of rotation of the conduit center atthe driver location. The angular amplitude of vibration, Δθ, isdetermined from the following relation:Δθ=arc tan(ΔZ/d)  (1)

The offset of the driver component (magnet or coil assembly) center ofmass from the conduit centerline causes the driver component center ofmass to have a Y-component of its vibration. The driver component massusually has an offset in the Z-direction that is at least equal to theconduit radius. The angular offset, φ, from the conduit centerline isthus not negligible. The driver component mass oscillates about itsoffset position with the same angular amplitude as the flow conduit, Δθ.Approximating the motion of the driver mass as being perpendicular tothe line connecting the driver center of mass with the center ofrotation, CR, the driver mass Y-direction motion, ΔY_(m), can be solvedfrom the following:ΔY _(m) =ΔZ sin(φ)  (2)

The Y-direction motion of the driver component mass causes the wholemeter to vibrate in the Y-direction. Conservation of momentum requiresthat, for a freely suspended meter, the Y-direction vibration of theentire meter is equal to the Y-direction vibration amplitude of thedriver mass times the ratio of the driver mass divided by the metermass. This Y-vibration of the entire meter is a direct result of thedesired conduit vibration in Z in conjunction with the angular offset ofthe drive components' centers of mass. This coupling between the desiredconduit vibration and the undesired Y-vibration of the entire metermeans that damping of the meter Y-vibration damps the flow conduitvibration in Z, and that a stiff meter mount raises conduit frequencywhile a soft meter mount lowers conduit frequency. The change in conduitfrequency with mounting stiffness has been observed experimentally inmeters with high Y-vibration amplitude. It is a problem because conduitfrequency is used to determine fluid density and frequency is also anindication of conduit stiffness. Changes in conduit stiffness due tomounting stiffness change the calibration factor of the meter. Thedirect coupling between the drive vibration and the local environmentalso results in an unstable zero (a flow signal when no flow is present)of the meter.

SUMMARY OF THE SOLUTION

The present invention helps solve the problems associated withunbalanced vibrational forces using a balance system that is sized andlocated so as to balance out the drive system. Advantageously, in someembodiments the invention can maintain a substantially constant massflow calibration factor over a wide range of possible flow materialdensities.

Some examples of a balance system include two or more Y-balance weightsand two or more attachment members that couple the two or more Y-balanceweights to a flow conduit. At least a first Y-balance weight is coupledto the flow conduit at a first location between the first conduit nodeand the drive system and at least a second Y-balance weight is coupledto flow conduit at a second location between the drive system and thesecond conduit node. The two or more Y-balance weights are sized andlocated such that the combined center of mass of the driver plus the twoor more Y-balance weights lies substantially on the X-Y plane of theconduit centerline.

In some examples, two or more balance devices, called active-y-balances,can be configured on the flow conduit(s). An active-y-balance comprisesa mass connected to one end of an attachment member, with the other endof the attachment member being attached to the flow conduit between thedriver and a bending axis W. Active-y-balances can be used on one orboth conduits depending on the locations of the mass centers of themagnet and coil and the type of flow meter configuration (i.e., singleor dual conduits).

An active-y-balance works by using the Z-direction conduit motion tomove the active-y-balance mass in the Y-direction. The Y-directionmomentum of the active-y-balance can be designed to balance theY-direction momentum of the drive components and to thereby preventunwanted case and environment motion. By the principle of equivalence,this also makes the meter immune to environmental vibrations anddamping.

Aspects

An aspect of the invention is a Coriolis flow meter comprising:

at least one flow conduit, with the at least one flow conduit includinga first conduit node and a second conduit node and including a bendingaxis W that intersects the flow conduit at the first conduit node and atthe second conduit node, wherein the at least one flow conduit vibratesaround the bending axis W;

a drive system coupled to the at least one flow conduit; and

a balance system coupled to the at least one flow conduit, with thebalance system comprising two or more Y-balance weights and two or moreattachment members that couple the two or more Y-balance weights to theat least one flow conduit, wherein at least a first Y-balance weight iscoupled to the at least one flow conduit at a first location between thefirst conduit node and the drive system and at least a second Y-balanceweight is coupled to the at least one flow conduit at a second locationbetween the drive system and the second conduit node.

Preferably the drive system is located a vertical distance Y_(d) abovethe bending axis W, the first Y-balance weight is located a verticaldistance Y_(w1) above the bending axis W, and the second Y-balanceweight is located a vertical distance Y_(w2) above the bending axis W.

Preferably a first ratio Y_(d)/Y_(w1) is substantially one and one-half.

Preferably a first ratio Y_(d)/Y_(w1) is substantially equal to a secondratio Y_(d)/Y_(w2).

Preferably a first ratio Y_(d)/Y_(w1) and a second ratio Y_(d)/Y_(w2)are configured so that a drive frequency versus twist frequency ratioω_(DRIVE)/ω_(TWIST) is substantially constant over changes in fluiddensity of a flow medium in the at least one flow conduit.

Preferably the two or more Y-balance weights and the two or moreattachment members are permanently coupled to the at least one flowconduit.

Preferably the two or more Y-balance weights and the two or moreattachment members are removably coupled to the at least one flowconduit.

Preferably the two or more attachment members are at least partiallydeformable in response to motion of the at least one flow conduit.

Preferably a deformation of the two or more attachment members and thetwo or more Y-balance weights cause the natural frequency of the balancesystem to be less than the drive frequency of the flow meter.

Preferably the balance system vibrates substantially out of phase withthe at least one flow conduit.

Preferably the balance system is sized and located such that thecombined center of mass of the drive system and the balance system liessubstantially proximate a plane of the centerline of the at least oneflow conduit.

Preferably the balance system is located on the substantially oppositeside of the at least one flow conduit from the drive system.

Preferably the balance system is located on the substantially oppositeside of the at least one flow conduit from the drive system and at anorientation substantially forty-five degrees to a horizontal plane ofthe flow conduit.

Preferably the balance system is sized and located such that themomentum of the balance system is substantially equal and substantiallyopposite to the momentum of the drive system in a directionsubstantially perpendicular to a drive motion.

Preferably a mass M_(split) of an individual Y-balance weight comprisessubstantially one-half of a mass of a single, driver-located weightM_(single) multiplied by the cube of a vertical distance Y_(d) of thedrive system above the bending axis W divided by a vertical distanceY_(w) of the individual Y-balance weight above the bending axis W.

An additional aspect of the invention is a method for force balancing aCoriolis flow meter, the method comprising:

providing at least one flow conduit, with the at least one flow conduitincluding a first conduit node and a second conduit node and furtherincluding a bending axis W that intersects the flow conduit at the firstconduit node and at the second conduit node, wherein the at least oneflow conduit vibrates around the bending axis W;

providing a drive system coupled to the at least one flow conduit; and

providing a balance system coupled to the at least one flow conduit,with the balance system comprising two or more Y-balance weights and twoor more attachment members that couple the two or more Y-balance weightsto the at least one flow conduit, wherein at least a first Y-balanceweight is coupled to the at least one flow conduit at a first locationbetween the first conduit node and the drive system and at least asecond Y-balance weight is coupled to the at least one flow conduit at asecond location between the drive system and the second conduit node.

Preferably the drive system is located a vertical distance Y_(d) abovethe bending axis W, the first Y-balance weight is located a verticaldistance Y_(w1) above the bending axis W, and the second Y-balanceweight is located a vertical distance Y_(w2) above the bending axis W.

Preferably a first ratio Y_(d)/Y_(w1) is substantially one and one-half.

Preferably a first ratio Y_(d)/Y_(w1) is substantially equal to a secondratio Y_(d)/Y_(w2).

Preferably a first ratio Y_(d)/Y_(w1) and a second ratio Y_(d)/Y_(w2)are configured so that a drive frequency versus twist frequency ratioω_(DRIVE)/ω_(TWIST) is substantially constant over changes in fluiddensity of a flow medium in the at least one flow conduit.

Preferably the two or more Y-balance weights and the two or moreattachment members are permanently coupled to the at least one flowconduit.

Preferably the two or more Y-balance weights and the two or moreattachment members are removably coupled to the at least one flowconduit.

Preferably the two or more attachment members are at least partiallydeformable in response to motion of the at least one flow conduit.

Preferably a deformation of the two or more attachment members and thetwo or more Y-balance weights cause the natural frequency of the balancesystem to be less than the drive frequency of the flow meter.

Preferably the balance system vibrates substantially out of phase withthe at least one flow conduit.

Preferably the balance system is sized and located such that thecombined center of mass of the drive system and the balance system liessubstantially proximate a plane of the centerline of the at least oneflow conduit.

Preferably the balance system is located on the substantially oppositeside of the at least one flow conduit from the drive system.

Preferably the balance system is located on the substantially oppositeside of the at least one flow conduit from the drive system and at anorientation substantially forty-five degrees to a horizontal plane ofthe flow conduit.

Preferably the balance system is sized and located such that themomentum of the balance system is substantially equal and substantiallyopposite to the momentum of the drive system in a directionsubstantially perpendicular to a drive motion.

Preferably a mass M_(split) of an individual Y-balance weight comprisessubstantially one-half of a mass of a single, driver-located weightM_(single) multiplied by the cube of a vertical distance Y_(d) of thedrive system above the bending axis W divided by a vertical distanceY_(w) of the individual Y-balance weight above the bending axis W.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a Coriolis flow meter comprising a flow meterassembly and meter electronics;

FIG. 2 illustrates a drive system in one embodiment of a Coriolis flowmeter;

FIG. 3 illustrates an X-axis section view of a flow conduit of aCoriolis meter;

FIG. 4 illustrates a balance system in a first example of the invention;

FIG. 5 illustrates a balance system in another example of the invention;and

FIG. 6 illustrates a balance system in yet another example of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1-5 and the following description depict specific examples toteach those skilled in the art how to make and use the best mode of theinvention. For the purpose of teaching inventive principles, someconventional aspects have been simplified or omitted. Those skilled inthe art will appreciate variations from these examples that fall withinthe scope of the invention. Those skilled in the art will appreciatethat the features described below can be combined in various ways toform multiple variations of the invention. As a result, the invention isnot limited to the specific examples described below, but only by theclaims and their equivalents.

FIG. 1 illustrates a Coriolis flow meter 5 comprising a flow meterassembly 10 and meter electronics 20. Meter electronics 20 is connectedto meter assembly 10 via leads 100 to provide density, mass flow rate,volume flow rate, totalized mass flow, temperature, and otherinformation over path 26. It should be apparent to those skilled in theart that the present invention can be used by any type of Coriolis flowmeter regardless of the number of drivers, pick-off sensors, flowconduits or the operating mode of vibration.

Flow meter assembly 10 includes a pair of flanges 101 and 101′;manifolds 102 and 102′; driver 104; pick-off sensors 105-105′; and flowconduits 103A and 103B. Driver 104 and pick-off sensors 105 and 105′ areconnected to flow conduits 103A and 103B. The flow meter assembly 10 canalso include a temperature sensor (not shown).

Flanges 101 and 101′ are affixed to manifolds 102 and 102′. Manifolds102 and 102′ are affixed to opposite ends of spacer 106. Spacer 106maintains the spacing between manifolds 102 and 102′ to preventundesired vibrations in flow conduits 103A and 103B. When flow meterassembly 10 is inserted into a pipeline system (not shown) which carriesthe material being measured, material enters flow meter assembly 10through flange 101, passes through inlet manifold 102 where the totalamount of material is directed to enter flow conduits 103A and 103B,flows through flow conduits 103A and 103B and back into outlet manifold102′ where it exits meter assembly 10 through flange 101′.

Flow conduits 103A and 103B are selected and appropriately mounted toinlet manifold 102 and outlet manifold 102′ so as to have substantiallythe same mass distribution, moments of inertia, and elastic modulesabout bending axes W-W and W′-W′ respectively. The flow conduits extendoutwardly from the manifolds in an essentially parallel fashion.

Flow conduits 103A-B are driven by driver 104 in opposite directionsabout their respective bending axes W and W′ and at what is termed thefirst out-of-phase bending mode of the flow meter. Driver 104 maycomprise one of many well known arrangements, such as a magnet mountedto flow conduit 103A and an opposing coil mounted to flow conduit 103B.An alternating current is passed through the opposing coil to cause bothconduits to oscillate. A suitable drive signal is applied by meterelectronics 20, via lead 110 to driver 104. The description of FIG. 1 isprovided merely as an example of the operation of a Coriolis flow meterand is not intended to limit the teaching of the present invention.

Meter electronics 20 receives sensor signals on leads 111 and 111′,respectively. Meter electronics 20 produces a drive signal on lead 110which causes driver 104 to oscillate flow conduits 103A and 103B. Meterelectronics 20 processes left and right velocity signals from pick-offsensors 105, 105′ in order to compute a mass flow rate. Path 26 providesan input and an output means that allows meter electronics 20 tointerface with an operator.

FIG. 2 illustrates a drive system 104 in one embodiment of a Coriolisflow meter 5. In a preferred exemplary embodiment, driver 104 is a coiland magnet assembly. One skilled in the art will note that other typesof drive systems may be used.

Driver 104 has a magnet assembly 210 and a coil assembly 220. Brackets211 extend outward in opposing directions from magnet assembly 210 andcoil assembly 220. Brackets 211 are wings which extend outward from theflat base and have a substantially curved edge 290 on a bottom side thatis formed to receive a flow conduit 103A or 103B. The curved edge 290 ofbrackets 211 are then welded or in some other manner affixed to flowconduits 103A and 103B to attach driver 104 to Coriolis flow meter 5.

Magnet assembly 210 has a magnet keeper 202 as a base. Brackets 211extend from a first side of magnet keeper 202. Walls 213 and 214 extendoutward from outer edges of a second side of magnet keeper 202. Walls213 and 214 control the direction of the magnetic field of magnet 203perpendicular to the windings of coil 204.

Magnet 203 is a substantially cylindrical magnet having a first and asecond end. Magnet 203 is fitted into a magnet sleeve (not shown). Themagnet sleeve and magnet 203 are affixed to a second surface of magnetkeeper 202 to secure magnet 203 in magnet assembly 210. Magnet 203typically has a pole (not shown) affixed to its second side. The magnetpole (not shown) is a cap that is fitted to the second end of magnet 203to direct the magnetic fields into coil 204.

Coil assembly 220 includes coil 204, and coil bobbin 205. Coil bobbin205 is affixed to a bracket 211. Coil bobbin 205 has a spool protrudingfrom a first surface around which coil 204 is wound. Coil 204 is mountedon coil bobbin 205 opposing magnet 203. Coil 204 is connected to lead110 which applies alternating currents to coil 204. The alternatingcurrents cause coil 204 and magnet 203 to attract and repel one anotherwhich in turn causes flow conduits 103A and 103B to oscillate inopposition to one another.

FIG. 3 illustrates a simplified X-axis section view of flow conduit 103.Flow conduit 103 has mounted to it driver 104. Driver 104 is offset fromflow conduit 103 by φ. Flow conduit 103 moves in the Z-direction with anamplitude ΔZ. As flow conduit 103 translates in the Z-direction itsfixed location causes it to rotate about its center of rotation, CR,resulting in angular amplitude, Δθ. Driver 104 and its associated centerof mass, CM, rotates with the same angular amplitude, Δθ, as flowconduit 103. However, because of the offset angle, φ, drive componentcenter of mass CM oscillates up and down line L. This gives drivecomponent center of mass CM vertical motion ΔY_(m).

FIG. 4 illustrates a balance system 400 in a first example of theinvention. Balance system 400 includes Y-balance weights 401 & 402coupled to flow conduits 103A & B. Coupling of Y-balance weights 401 &402 can be accomplished using various methods including mechanicalattachment, welding, brazing, or gluing. Y-balance weight 401 has acenter of mass CM_(b1). Y-balance weight 401 is sized and located suchthat its center of mass CM_(b1) combined with the coil assembly centerof mass CM_(c) results in a combined center of mass CCM₁ that is locatedon the X-Y plane of conduit 103A. Also, Y-balance weight 402 has acenter of mass CM_(b2). Y-balance weight 402 is sized and located suchthat its center of mass CM_(b2) combined with the magnet assembly centerof mass CM_(m) results in a combined center of mass CCM₂ that is locatedon the X-Y plane of conduit 103B. The particular attributes of theY-balance weights are such that the mass times velocity of the Y-balanceweight is equal and opposite to the mass times velocity of the driverassembly, in the Y-direction, for each flow conduit as shown by:(M*V _(Y))_(BW)+(M*V _(Y))_(DA)=0  (3)In other words the momentum of the Y-balance weight counters themomentum of the driver assembly attached to a particular conduit asgiven by:(M _(BW))_(Y)+(M _(DA))_(Y)=0  (4)

FIG. 5 illustrates balance system 500 in another example of theinvention. Balance system 500 includes Y-balance weights 501 & 502coupled to flow conduits 103A & B using leaf springs 504 & 505. Leafspring 504 in this embodiment is oriented at approximately 45 degrees tothe X-Y plane and is connected to the opposite side of the flow conduitas coil assembly 220. The stiffness of leaf spring 504 and mass ofY-balance weight 501 are chosen so that the natural frequency of theactive-y-balance in its first vibration mode (the diving board mode) isbelow the drive frequency of the meter. With the natural frequency belowthe excitation (drive) frequency, weight 501 tends to move out of phasewith conduit 103A. Thus, as conduit 103A moves to the left (−Zdirection), active-Y-balance weight 501 moves to the right (+Z) relativeto the conduit. But, because of the angle of leaf spring 504 to the X-Yplane, weight 501 is constrained by leaf spring 504 to move to the rightand down (+Z and −Y). This is advantageous because when conduit 103Amoves to the left, the offset coil assembly 220 moves left and up (+Zand +Y). By designing mass and spring rate such that the Y-directionmomentum (mass times velocity) of the active-y-balance are equal andopposite to the Y-direction momentum of the offset driver components,the external Y-direction vibration of the entire meter can be nearlyeliminated. The same design principles apply to tube 103B.

This second example has an additional advantage. Because weight 501 and502 are suspended from conduits 103A & B by leaf spring 504 & 505, theyvibrate out of phase with flow conduits 103A & B, resulting in verylittle of its mass being coupled to flow conduits 103A & B.

It should be understood that the angle and orientation of the leafsprings 504 and weights 501 in the figure are given for example. Theangle and orientation of the leaf springs 504 and weights 501 can bevaried and still achieve the goals of the invention.

FIG. 6 illustrates a balance system 600 in yet another example of theinvention. In this embodiment, the balance system 600 includes the flowconduit 103 having a first conduit node 603 a and a second conduit node603 b, the drive system 104, pickoffs 105 and 105′, at least first andsecond Y-balance weights 601 a and 601 b, and at least first and secondattachment members 602 a and 602 b. The pickoffs 105 and 105′ arelocated between the drive system 104 and the first conduit node 603 aand the second conduit node 603 b. It should be understood that theshape of the flow conduit 103 in the figure is given for example, andthe flow conduit 103 can comprise other geometries. It should also beunderstood that the locations of the Y-balance weights 601 a and 601 bare also examples, and the locations can vary according to the flow tubematerial, the flow tube geometry, the flow material, temperature, drivervibration, driver mass, pick-off mass, construction tolerances, etc.

The flow conduit 103 can comprise a single conduit flow meter or cancomprise a component of a two conduit flow meter (see FIG. 5). The flowconduit 103 vibrates around a bending axis W (see also the center ofrotation CR in FIG. 3). The bending axis W intersects the flow conduitat the first conduit node 603 a and at the second conduit node 603 b.

The Y-balance weights 601 and attachment members 602 are coupled to theflow conduit 103. A first Y-balance weight 601 a and a first attachmentmember 602 a can be coupled to the flow conduit 103 between the firstconduit node 603 a and the drive system 104. Likewise, a secondY-balance weight 601 b and a second attachment member 602 b can becoupled to the flow conduit 103 between the drive system 104 and thesecond conduit node 603 b. The first Y-balance weight 601 a and thesecond Y-balance weight 601 b can be permanently or removably coupled tothe flow conduit 103 by the corresponding first attachment member 602 aand second attachment member 602 b. In addition, a removably coupledattachment member 602 can comprise a slidably coupled attachment member602 that can be slidably positioned on the flow conduit 103.

Two or more Y-balance weights 601 are used in order to accurately andeffectively perform Y-balancing of the flow meter 5, but withoutaffecting a flow calibration characteristic of the flow meter 5. Aproblem that is encountered with a single Y-balance weight, attached ata single point on the flow conduit 103, is that the flow calibrationfactor can shift when the flow meter 5 is used for fluids of differentdensities. In order for the flow meter 5 to have a flow calibrationfactor that is independent of fluid density, the distribution of massadded to the flow conduit 103 has to be such that a drive frequency totwist frequency ratio (i.e., ω_(DRIVE)/ω_(TWIST)) remains constant overany and all changes in fluid density.

In a typical U-tube flow meter, the flow conduit 103 is vibrated at adrive frequency. The drive frequency is chosen to substantially match aresonant frequency of the flow conduit 103. The resulting drive modevibration (i.e., a first out-of-phase bending mode) includes stationarynodes at the ends of the flow conduit 103, while the point of maximumvibrational amplitude occurs at the center of the flow conduit 103,i.e., at the drive system 104. For example, these end nodes can comprisethe nodes 603 a and 603 b shown in FIG. 6.

The twist mode of vibration is excited by the Coriolis force resultingfrom fluid flow. It is the tube vibration in the twist mode that createsthe time delay that is measured by the electronics. In a twist mode ofvibration (i.e., a second out-of-phase bending mode), the flow conduit103 has stationary nodes at the ends of the flow conduit andadditionally includes a stationary node at the center (i.e., at thedrive system 104). Consequently, in the twist mode the maximum amplitudeof the flow conduit 103 occurs at two points located between the drivesystem 104 and the end nodes.

The twist mode has a twist resonant frequency that is generally higherthan the drive frequency. However, the Coriolis force is of greatestamplitude at the drive frequency, rather than the higher twistfrequency, and is preferably measured at the drive frequency. Theresonant frequency of the twist mode of vibration is generally higherthan the resonant frequency of the drive mode of vibration. Therefore,the resulting amplitude of vibration is a function of the frequencydifference between the drive frequency and the twist resonant frequency.If the two frequencies are close, the twist amplitude is large. If theyare distant, the twist amplitude is small. It can thus be seen that afrequency ratio between the drive frequency and the twist resonantfrequency must be kept constant in order to keep the flow calibrationfactor of the flow meter at a constant level.

The drive and twist frequencies both change when the fluid densitychanges. The location of mass on the flow tube determines whether thefrequency ratio remains constant between the two. Because the drive modein a typical U-tube flow meter includes nodes at the ends of the flowconduit 103 and because the point of maximum amplitude occurs in thecenter, locating extra mass at the drive system 104 has the effect oflowering the drive frequency and reducing the effect of fluid densitychange on the drive frequency. In the twist mode, where there are nodesat both ends of each flow tube as well as one in the center, locatingextra mass at the drive system 104 does not affect the twist modebecause of the central node. However, locating mass at the points ofmaximum deflection in the twist mode (between the drive system 104 andthe end nodes) reduces the twist mode sensitivity to changes in fluiddensity.

The solution to this drawback is to form a balance system 600 includingat least two spaced apart Y-balance weights 601 on either side of thedrive system 104. The at least two Y-balance weights 601 are locatedupstream and downstream from the drive system 104, as shown in thefigure. The mass for the Y-balance weights can thus be located at adistance from the drive system 104 so that the drive and twistfrequencies both change the proper amount with changes in fluid density.This distance from the drive system 104 can be determined, such asthrough finite element analysis, for example, and has been determined tobe the distance at which the ratio of frequencies (ω_(DRIVE)/ω_(TWIST))stays constant with changes in fluid density. Simultaneously, theseweights can be sized so that they are correct for Y-balancing the meter.

The drive system 104 is located a vertical distance Y_(d) above thebending axis W. The first Y-balance weight 601 a is located a verticaldistance Y_(w1) above the bending axis W. The second Y-balance weight601 b is located a vertical distance Y_(w2) above the bending axis W.The two or more Y-balance weights 601 a and 601 b are therefore locatedaccording to a Y distance ratio Y_(d)/Y_(w1) and Y_(d)/Y_(w2), forexample. In one embodiment, one or both of the ratios can besubstantially one and one-half (i.e., Y_(d)/Y_(w)=1½). In anotherembodiment having a different flow tube geometry (and other factors),the ratios can be substantially two. However, other values can be usedas desired. In one embodiment, the first ratio Y_(d)/Y_(w1) issubstantially equal to the second ratio Y_(d)/Y_(w2) (i.e.,Y_(d)/Y_(w1)=Y_(d)/Y_(w2)). However, it should be understood that thedistances can vary according to flow conduit size and characteristics,construction tolerances, etc., and the distances therefore can form anysize of ratio. Moreover, the two ratios Y_(d)/Y_(w1) and Y_(d)/Y_(w2)can differ, and are not necessarily equal.

The actual locations of the Y-balance weights 601, and therefore thedistances Y_(w1) and Y_(w2), can be determined experimentally or can beiteratively determined using a Finite Element Analysis (FEA) technique,for example. The desired FEA result maintains a substantially constantω_(DRIVE)/ω_(TWIST) ratio over changes in fluid density of a flow mediumin the flow conduit 103. The desired FEA therefore constrains theY-motion to an acceptable level. In one embodiment, an approximatestarting point for the FEA computation initially locates the Y-balanceweights 601 half-way vertically to the pickoffs 105 and 105′ (i.e., thedistance ratios Y_(d)/Y_(w1) and Y_(d)/Y_(w2) are approximately=2 andcreates an angle from the horizontal that is approximately 45 degrees).

In addition, the mass of each Y-balance weight 601 will have to becalculated when the location has been determined. The mass M_(split) ofeach individual split Y-balance weight 601 will need to be greater thanthe mass M_(single) of a single Y-balance weight located at the drivesystem 104 in order to achieve the same mass balancing effect. The massM_(split) of an individual Y-balance weight 601 a or 601 b can beapproximately determined through use of the formula:M _(split)=½(M _(single))(Y _(d) /Y _(w))³  (5)Consequently, as the vertical distance Y_(w) decreases, the aboveformula will cause the mass M_(split) to increase.

As in the previously discussed Y-balance weight 501 and leaf spring 504of FIG. 5, the attachment members 602 a and 602 b can be at leastpartially deformable. For example, an attachment member 602 can comprisea spring or leaf spring. Consequently, the attachment members 602 a and602 b can deform in response to motion of the flow conduit 103. Thedeformation of the two or more attachment members 602 and the two ormore Y-balance weights 601 cause the natural frequency of the balancesystem 600 to be less than the drive frequency of the flow meter 5. As aresult, the balance system 600 can vibrate out of phase with the flowconduit 103.

The balance system 600 in one embodiment is sized and located such thatthe combined center of mass of the drive system 104 and the balancesystem 600 lies substantially proximate a plane of the centerline of theflow conduit 103. In one embodiment, the balance system 600 is locatedon the substantially opposite side of the flow conduit 103 from thedrive system 104 (see FIG. 5). In one embodiment, the balance system 600is located on the substantially opposite side of the flow conduit 103from the drive system 104 and at an orientation substantially forty-fivedegrees to a horizontal plane of the flow conduit 103. The balancesystem 600 in one embodiment is sized and located such that the momentumof the balance system 600 is substantially equal and opposite to themomentum of the drive system 104 in a direction substantiallyperpendicular to a drive motion.

It should be understood that more than two Y-balance weights 601 can beused in order to accomplish the objectives of the invention. Inaddition, various numbers and configurations of attachment members 602can be employed. The attachment members 602 can include cross-linksbetween Y-balance weights 601, can include multiple attachment members602 per Y-balance weight 601, can include variously shaped or sizedattachment members 602, can include attachment members 602 formed ofdifferent materials, can include attachment members 602 having differentdeformation characteristics, etc.

The above examples are not limited to compensating for the driver massoffset. For instance, deformation of the manifold castings by conduitforces can cause the meter flanges to vibrate in the Y-direction. Ifthis flange vibration is in-phase with that caused by the drive massoffset, then the balance mass can be increased to compensate for theadditional vibration due to the manifold deformation. Likewise, if theflange vibration due to manifold deformation is out-of-phase with thatcaused by the drive mass offset, the balance mass can be made smaller.

1. A Coriolis flow meter comprising: at least one flow conduit (103),with the at least one flow conduit (103) including a first conduit node(603 a) and a second conduit node (603 b) and including a bending axis Wthat intersects the flow conduit (103) at the first conduit node (603 a)and at the second conduit node (603 b), wherein the at least one flowconduit (103) vibrates around the bending axis W; a drive system (104)coupled to the at least one flow conduit (103); and a balance system(600) coupled to the at least one flow conduit (103), with the balancesystem (600) comprising two or more Y-balance weights (601 a, 601 b) andtwo or more attachment members (602 a, 602 b) that couple the two ormore Y-balance weights (601 a, 601 b) to the at least one flow conduit(103), wherein at least a first Y-balance weight (601 a) is coupled tothe at least one flow conduit (103) at a first location between thefirst conduit node (603 a) and the drive system (104) and at least asecond Y-balance weight (601 b) is coupled to the at least one flowconduit (103) at a second location between the drive system (104) andthe second conduit node (603 b).
 2. The Coriolis flow meter of claim 1wherein the drive system (104) is located a vertical distance Y_(d)above the bending axis W, wherein the first Y-balance weight (601 a) islocated a vertical distance Y_(w1) above the bending axis W, and whereinthe second Y-balance weight (601 b) is located a vertical distanceY_(w2) above the bending axis W.
 3. The Coriolis flow meter of claim 2wherein a first ratio Y_(d)/Y_(w1) is substantially one and one-half toone (Y_(d)/Y_(w1)=1½:1).
 4. The Coriolis flow meter of claim 2 wherein afirst ratio Y_(d)/Y_(w1) is substantially equal to a second ratioY_(d)/Y_(w2).
 5. The Coriolis flow meter of claim 2 wherein a firstratio Y_(d)/Y_(w1) and a second ratio Y_(d)/Y_(w2) are configured sothat a drive frequency versus twist frequency ratio ω_(DRIVE)/ω_(TWIST)is substantially constant over changes in fluid density of a flow mediumin the at least one flow conduit (103).
 6. The Coriolis flow meter ofclaim 1 wherein the two or more Y-balance weights (601 a, 601 b) arelocated at points of maximum deflection of the at least one conduit(103) in a twist mode.
 7. The Coriolis flow meter of claim 1 wherein thetwo or more Y-balance weights (601 a, 601 b) and the two or moreattachment members (602 a, 602 b) are permanently coupled to the atleast one flow conduit (103).
 8. The Coriolis flow meter of claim 1wherein the two or more Y-balance weights (601 a, 601 b) and the two ormore attachment members (602 a, 602 b) are removably coupled to the atleast one flow conduit (103).
 9. The Coriolis flow meter of claim 1wherein the two or more attachment members (602 a, 602 b) are at leastpartially deformable in response to motion of the at least one flowconduit (103).
 10. The Coriolis flow meter of claim 1 wherein adeformation of the two or more attachment members (602 a, 602 b) and thetwo or more Y-balance weights (601 a, 601 b) cause the natural frequencyof the balance system (600) to be less than the drive frequency of theflow meter.
 11. The Coriolis flow meter of claim 1 wherein the balancesystem (600) vibrates substantially out of phase with the at least oneflow conduit (103).
 12. The Coriolis flow meter of claim 1 wherein thebalance system (600) is sized and located such that the combined centerof mass of the drive system (104) and the balance system (600) liessubstantially proximate a plane of the centerline of the at least oneflow conduit (103).
 13. The Coriolis flow meter of claim 1 wherein thebalance system (600) is located on the substantially opposite side ofthe at least one flow conduit (103) from the drive system (104).
 14. TheCoriolis flow meter of claim 1 wherein the balance system (600) islocated on the substantially opposite side of the at least one flowconduit (103) from the drive system (104) and at an orientationsubstantially forty-five degrees to a horizontal plane of the flowconduit (103).
 15. The Coriolis flow meter of claim 1 wherein thebalance system (600) is sized and located such that the momentum of thebalance system (600) is substantially equal and substantially oppositeto the momentum of the drive system (104) in a direction substantiallyperpendicular to a drive motion.
 16. The Coriolis flow meter of claim 1wherein a mass M_(split) of an individual Y-balance weight (601)comprises substantially one-half of a mass of a single, driver-locatedweight M_(single) multiplied by the cube of a vertical distance Y_(d) ofthe drive system (104) above the bending axis W divided by a verticaldistance Y_(w) of the individual Y-balance weight (601) above thebending axis W.
 17. A method for force balancing a Coriolis flow meter,the method comprising: providing at least one flow conduit (103), withthe at least one flow conduit (103) including a first conduit node (603a) and a second conduit node (603 b) and further including a bendingaxis W that intersects the flow conduit (103) at the first conduit node(603 a) and at the second conduit node (603 b), wherein the at least oneflow conduit (103) vibrates around the bending axis W; providing a drivesystem (104) coupled to the at least one flow conduit (103); andproviding a balance system (600) coupled to the at least one flowconduit (103), with the balance system (600) comprising two or moreY-balance weights (601 a, 601 b) and two or more attachment members (602a, 602 b) that couple the two or more Y-balance weights (601 a, 601 b)to the at least one flow conduit (103), wherein at least a firstY-balance weight (601 a) is coupled to the at least one flow conduit(103) at a first location between the first conduit node (603 a) and thedrive system (104) and at least a second Y-balance weight (601 b) iscoupled to the at least one flow conduit (103) at a second locationbetween the drive system (104) and the second conduit node (603 b). 18.The method of claim 17 wherein the drive system (104) is located avertical distance Y_(d) above the bending axis W, wherein the firstY-balance weight (601 a) is located a vertical distance Y_(w1) above thebending axis W, and wherein the second Y-balance weight (601 b) islocated a vertical distance Y_(w2) above the bending axis W.
 19. Themethod of claim 18 wherein a first ratio Y_(d)/Y_(w1) is substantiallyone and one-half to one (Y_(d)/Y_(w1)=1½:1).
 20. The method of claim 18wherein a first ratio Y_(d)/Y_(w1) is substantially equal to a secondratio Y_(d)/Y_(w2).
 21. The method of claim 18 wherein a first ratioY_(d)/Y_(w1) and a second ratio Y_(d)/Y_(w2) are configured so that adrive frequency versus twist frequency ratio ω_(DRIVE)/ω_(TWIST) issubstantially constant over changes in fluid density of a flow medium inthe at least one flow conduit (103).
 22. The method of claim 17 whereinthe two or more Y-balance weights (601 a, 601 b) are located at pointsof maximum deflection of the at least one conduit (103) in a twist mode.23. The method of claim 17 wherein the two or more Y-balance weights(601 a, 601 b) and the two or more attachment members (602 a, 602 b) arepermanently coupled to the at least one flow conduit (103).
 24. Themethod of claim 17 wherein the two or more Y-balance weights (601 a, 601b) and the two or more attachment members (602 a, 602 b) are removablycoupled to the at least one flow conduit (103).
 25. The method of clan17 wherein the two or more attachment members (602 a, 602 b) are atleast partially deformable in response to motion of the at least oneflow conduit (103).
 26. The method of claim 17 wherein a deformation ofthe two or more attachment members (602 a, 602 b) and the two or moreY-balance weights (601 a, 601 b) cause the natural frequency of thebalance system (600) to be less than the drive frequency of the flowmeter.
 27. The method of claim 17 wherein the balance system (600)vibrates substantially out of phase with the at least one flow conduit(103).
 28. The method of claim 17 wherein the balance system (600) issized and located such that the combined center of mass of the drivesystem (104) and the balance system (600) lies substantially proximate aplane of the centerline of the at least one flow conduit (103).
 29. Themethod of claim 17 wherein the balance system (600) is located on thesubstantially opposite side of the at least one flow conduit (103) fromthe drive system (104).
 30. The method of claim 17 wherein the balancesystem (600) is located on the substantially opposite side of the atleast one flow conduit (103) from the drive system (104) and at anorientation substantially forty-five degrees to a horizontal plane ofthe flow conduit (103).
 31. The method of claim 17 wherein the balancesystem (600) is sized and located such that the momentum of the balancesystem (600) is substantially equal and substantially opposite to themomentum of the drive system (104) in a direction substantiallyperpendicular to a drive motion.
 32. The method of claim 17 wherein amass M_(split) of an individual Y-balance weight (601) comprisessubstantially one-half of a mass of a single, driver-located weightM_(single) multiplied by the cube of a vertical distance Y_(d) of thedrive system (104) above the bending axis W divided by a verticaldistance Y_(w) of the individual Y-balance weight (601) above thebending axis W.